A complex manifold $X$ is hyperbolic if there are no nonconstant holomorphic maps $f:\mathbb{C} \to X$. A projective variety $X$ is quasi-hyperbolic if it has only finitely many rational and elliptic curves. The Kobayashi conjecture states that: The generic hypersurface of degree $d\ge 5$ in $\mathbb{P}^3$ is hyperbolic (hence also quasi-hyperbolic). Clemens proved quasi-hyperbolicity for very generic hypersurfaces. We show that nodal hypersurfaces with a sufficiently large number of nodes are also quasi-hyperbolic. An ingredient of the proof of this counter intuitive result is Bogomolov's theory of symmetric differentials.